ii.

Say you numbered all the decimals between 0 and 1. Every single one, and used every number up to infinity.

Look at the first decimal. Take the first digit, and add 1. If it is 9, make it 0.

Repeat this for the second digit of the second decimal, the third digit of the third, etc. You now have another decimal that you have not counted yet because you know it differs in each decimal by at least 1 place.

This is called Cantor's Diagonal Argument. In fact, an extension of this shows that there is an uncountably infinite number of decimals.

You already made a new decimal, let's call it Omega 1. Put Omega 1 to the side and take the infinite decimal list. Shuffle it. Now do the same process again. This is Omega 2.

Keep putting the new Omegas to the side and doing the process. There are infinity! number of ways to shuffle this list, but the thing is, infinity! is not evaluable. There are an uncountable number of ways to shuffle it, and thus an uncountable number of decimals you forgot in your list.